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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 16.2, Problem 56E

Textbook Problem

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Motion of a Spring In Exercise 55-58, match the differential equation with the graph of a particular solution. [The graphs are labeled (a), (b), (c) and (d).] The correct match can be made by comparing the frequency of the oscillations or the rate at which the oscillations are being damped with the appropriate coefficient in the differential equation.

To determine

The graph of the particular solution of the differential equation

**Given information:** The graphs,

Comparing the equation

Multivariable Calculus

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In exercises 67-70, determine...Ch. 16.2 - True or False? In exercises 67-70, determine...Ch. 16.2 - Wronskian The Wronskian of two differentiable...Ch. 16.2 - Wronskian The Wronskian of two differentiable...Ch. 16.2 - Wronskian The Wronskian of two differentiable...Ch. 16.2 - Wronskian The Wronskian of two differentiable...Ch. 16.3 - Writing What is the form of the general solution...Ch. 16.3 - Choosing a MethodDetermine whether you woulduse...Ch. 16.3 - Method of Undetermined Coefficients InExercises...Ch. 16.3 - Method of Undetermined Coefficients In Exercises...Ch. 16.3 - Method of Undetermined Coefficients In Exercises...Ch. 16.3 - Method of Undetermined Coefficients In Exercises...Ch. 16.3 - Choosing the Form of the ParticularSolution In...Ch. 16.3 - Choosing the Form of the ParticularSolution In...Ch. 16.3 - Choosing the Form of the Particular Solution In...Ch. 16.3 - Choosing the Form of the Particular Solution In...Ch. 16.3 - Method of Undetermined CoefficientsIn Exercises...Ch. 16.3 - Method of Undetermined CoefficientsIn Exercises...Ch. 16.3 - Method of Undetermined CoefficientsIn Exercises...Ch. 16.3 - Method of Undetermined CoefficientsIn Exercises...Ch. 16.3 - Method of Undetermined CoefficientsIn Exercises...Ch. 16.3 - Method of Undetermined CoefficientsIn Exercises...Ch. 16.3 - Using Initial Conditions In Exercises 17-22, solve...Ch. 16.3 - Using Initial Conditions In Exercises 17-22, solve...Ch. 16.3 - Using Initial Conditions In Exercises 17-22, solve...Ch. 16.3 - Using Initial Conditions In Exercises 17-22, solve...Ch. 16.3 - Using Initial Conditions In Exercises 17-22, solve...Ch. 16.3 - Using Initial Conditions In Exercises 17-22, solve...Ch. 16.3 - Method of Variation of Parameters InExercises...Ch. 16.3 - Method of Variation of Parameters In Exercises...Ch. 16.3 - Method of Variation of Parameters In Exercises...Ch. 16.3 - Method of Variation of Parameters In Exercises...Ch. 16.3 - Method of Variation of Parameters In Exercises...Ch. 16.3 - Method of Variation of Parameters In Exercises...Ch. 16.3 - Electrical Circuits In Exercises 29 and 30, use...Ch. 16.3 - Electrical Circuits In Exercises 29 and 30, use...Ch. 16.3 - Motion of a Spring In Exercises 31-34, use the...Ch. 16.3 - Motion of a Spring In Exercises 31-34, use the...Ch. 16.3 - Motion of a Spring In Exercises 31-34, use the...Ch. 16.3 - Motion of a Spring In Exercises 31-34, use the...Ch. 16.3 - EXPLORING CONCEPTS Motion of a Spring Rewrite yh...Ch. 16.3 - HOW DO YOU SEE IT? The figure shows the particular...Ch. 16.3 - Motion of a SpringRefer to the differential...Ch. 16.3 - Solving a Differential Equation Solve the...Ch. 16.3 - True or False? In Exercises 39 and 40, determine...Ch. 16.3 - True or False? In Exercises 39 and 40, determine...Ch. 16.3 - PUTNAM EXAM CHALLENGE For all real x, the...Ch. 16.4 - CONCEPT CHECK Power Series Solution Method...Ch. 16.4 - CONCEPT CHECK Recursion Formula What is a...Ch. 16.4 - Power Series Solution In Exercises 3-6, use a...Ch. 16.4 - Power Series Solution In Exercises 3-6, use a...Ch. 16.4 - Power Series Solution In Exercises 3-6, use a...Ch. 16.4 - Power Series Solution In Exercises 3-6, use a...Ch. 16.4 - Finding Terms of a Power Series SolutionIn...Ch. 16.4 - Finding Terms of a Power Series SolutionIn...Ch. 16.4 - Approximation by Taylor Series In Exercises 9-14,...Ch. 16.4 - Approximation by Taylor Series In Exercises 9-14,...Ch. 16.4 - Approximation by Taylor Series In Exercises 9-14,...Ch. 16.4 - Approximation by Taylor Series In Exercises 9-14,...Ch. 16.4 - Approximation by Taylor Series In Exercises 9-14,...Ch. 16.4 - Approximation by Taylor Series In Exercises 9-14,...Ch. 16.4 - EXPLORING CONCEPTS Using Different MethodsIn...Ch. 16.4 - EXPLORING CONCEPTS Using Different MethodsIn...Ch. 16.4 - EXPLORING CONCEPTS Using Different MethodsIn...Ch. 16.4 - EXPLORING CONCEPTS Using Different MethodsIn...Ch. 16.4 - Investigation Consider the differential equation...Ch. 16.4 - HOW DO YOU SEE IT? Consider the differential...Ch. 16.4 - Verifying that a Series Converges In Exercises...Ch. 16.4 - Verifying that a Series Converges In Exercises...Ch. 16.4 - Verifying that a Series Converges In Exercises...Ch. 16.4 - Verifying that a Series Converges In Exercises...Ch. 16.4 - Airys Equation Find the first six terms of the...Ch. 16 - Testing for Exactness In Exercises 1 and 2,...Ch. 16 - Testing for Exactness In Exercises 1 and 2,...Ch. 16 - Solving an Exact Differential Equation In...Ch. 16 - Solving an Exact Differential Equation In...Ch. 16 - Solving an Exact Differential Equation In...Ch. 16 - Solving an Exact Differential Equation In...Ch. 16 - Graphical and Analytical Analysis In Exercise 7...Ch. 16 - Graphical and Analytical Analysis In Exercise 7...Ch. 16 - Finding a Particular Solution In Exercises 9-12,...Ch. 16 - Finding a Particular Solution In Exercises 9-12,...Ch. 16 - Finding a Particular Solution In Exercises 9-12,...Ch. 16 - Finding a Particular Solution In Exercises 9-12,...Ch. 16 - Finding an Integrating Factor In Exercises 13-16,...Ch. 16 - Finding an Integrating Factor In Exercises 13-16,...Ch. 16 - Finding an Integrating Factor In Exercises 13-16,...Ch. 16 - Finding an Integrating Factor In Exercises 13-16,...Ch. 16 - Verifying a Solution In Exercises 17-18, verify...Ch. 16 - Verifying a Solution In Exercises 17 and 18,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a Particular Solution: Initial Conditions...Ch. 16 - 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Using Initial Conditions In Exercises 45-50, solve...Ch. 16 - Using Initial Conditions In Exercises 45-50, solve...Ch. 16 - Using Initial Conditions In Exercises 45-50, solve...Ch. 16 - Method of Variation of Parameters In Exercises...Ch. 16 - Method of Variation of Parameters In Exercises...Ch. 16 - Method of Variation of Parameters In Exercises...Ch. 16 - Method of Variation of Parameters In Exercises...Ch. 16 - Electrical Circuit The differential equation...Ch. 16 - Investigation The differential equation...Ch. 16 - Think About It (a) Explain how, by observation,...Ch. 16 - Think About It Explain how you can find a...Ch. 16 - Power Series Solution In Exercises 59 and 60, use...Ch. 16 - Power Series Solution In Exercises 59 and 60, use...Ch. 16 - Approximation by Taylor Series In Exercises 61 and...Ch. 16 - Approximation by Taylor Series In Exercises 61 and...Ch. 16 - Finding a General Solution Find the value of k...Ch. 16 - Using an Integrating Factor The differential...Ch. 16 - Finding a General Solution Find the general...Ch. 16 - 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